Construct Matrix

给你一个偶数 $n$ 和一个整数 $k$。你需要构造一个 $n\times n$ 的 $01$ 矩阵满足如下条件： - 矩阵所有数总和是 $k$。 - 每一行的 $XOR$ 值相同。 - 每一列的 $XOR$ 值相同。 有解给出构造，否则报告无解。 $2\le n\le 1000,0\le k\le n^2$。 多测，保证所有测试点的 $n$ 加起来不超过 $2000$。 By:Call_me_Eric

You are given an even integer $ n $ and an integer $ k $ . Your task is to construct a matrix of size $ n \times n $ consisting of numbers $ 0 $ and $ 1 $ in such a way that the following conditions are true, or report that it is impossible: - the sum of all the numbers in the matrix is exactly $ k $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the row $ i $ is the same for each $ i $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the column $ j $ is the same for each $ j $ .

Each test consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 130 $ ) — the number of test cases. The description of the test cases follows. Each test case is described by a single line, which contains two integers $ n $ and $ k $ ( $ 2 \leq n \leq 1000 $ , $ n $ is even, $ 0 \leq k \leq n^2 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2000 $ .

For each test case, output $ \texttt{Yes} $ if it's possible to construct a matrix that satisfies all of the problem's conditions, and $ \texttt{No} $ otherwise. If it is possible to construct a matrix, the $ i $ -th of the next $ n $ lines should contain $ n $ integers representing the elements in the $ i $ -th row of the matrix.

5
4 0
6 6
6 5
4 2
6 36

Yes
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
Yes
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
No
No
Yes
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1

In the first example, all conditions are satisfied: - the sum of all the numbers in the matrix is exactly $ 0 $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the row $ i $ is $ 0 $ for each $ i $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the column $ j $ is $ 0 $ for each $ j $ . In the third example, it can be shown that it's impossible to find a matrix satisfying all the problem's conditions.